A Time-Domain Green’s Function for Interaction between Water Waves and Floating Bodies with Viscous Dissipation Effects

Abstract

Abstract:A novel time-domain Green's function is developed for dealing with two-dimensional interaction between water waves and floating bodies with considering viscous dissipation effects based on the "fairly perfect fluid" model. In the Green's function, the temporal (lower order viscosity coefficient term) and spatial (higher order viscosity coefficient term) viscous dissipation effects are fully considered. As compared to the methods based on the existing time-domain Green's functions that could not account for the spatial viscous dissipation, the method based on the new time-domain Green's function can give much better numerical results and overcome instability problems related to the existing Green's function, according to the numerical tests and comparison with CFD modeling data for a few cases related to floating bodies with a flare angle.

A Body-Nonlinear Green’s Function Method with Viscous Dissipation Effects for Large-Amplitude Roll of Floating Bodies

“…From Equation (2), one can observe that in the definite conditions of the TGF_N _V, the normal velocity V n (t) is satisfied on the instantaneous wetted surface of the floating body, while the normal velocity in TGF_V [21] is given on the mean wetted surface S B (t) of the floating body. This difference makes the definite problem of the TGF_N _V to be body-nonlinear.…”

“…Analogous to the TGF_V [21], the Green's function method is employed to solve the Equation (2). Let G(p, t; q, τ; ) be the Green's function, which can be expressed as the combination of instantaneous term G(p, q; ) and free-surface memory term G(p, t; q, τ; ).…”

“…Obviously, the definite conditions given in Equation (4) are the same as those in Guo et al [21], i.e., they are not related to the body condition. Thereby, according to Guo et al [21], the expression of the free-surface memory term G(p, t; q, τ; ) is…”

“…More recently, Guo et al [21] first proposed a linear time-domain Green's function method (TGF_V) for assessing the interaction between floating bodies and water waves with viscous dissipation effects, which can accurately evaluate the hydrodynamic coefficients of sharply edged floating bodies with small roll amplitude. The TGF_V [21] can consider the full viscous dissipation effects of water, while other similar Green's functions [22][23][24] can only take the partial viscous dissipation effects into account.…”

“…The TGF_V [21] can consider the full viscous dissipation effects of water, while other similar Green's functions [22][23][24] can only take the partial viscous dissipation effects into account. However, the linear TGF_V or other Green's functions cannot be employed to evaluate the equivalent damping coefficient of large-amplitude roll motion, which is known to be highly nonlinear.…”